dorsal/arxiv
View SchemaThe Shapley Value of Phylogenetic Trees
| Authors | Claus-Jochen Haake, Akemi Kashiwada, Francis Edward Su |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0506034 |
| URL | https://arxiv.org/abs/q-bio/0506034 |
| DOI | 10.1007/s00285-007-0126-2 |
| Journal | J. Mathematical Biology 56 (2008), 479--497 |
Abstract
Every weighted tree corresponds naturally to a cooperative game that we call a "tree game"; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the leaves are species and this assignment captures the diversity present in the coalition of species considered. We consider the Shapley value of tree games and suggest a biological interpretation. We determine the linear transformation M that shows the dependence of the Shapley value on the edge weights of the tree, and we also compute a null space basis of M. Both depend on the "split counts" of the tree. Finally, we characterize the Shapley value on tree games by four axioms, a counterpart to Shapley's original theorem on the larger class of cooperative games.
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"abstract": "Every weighted tree corresponds naturally to a cooperative game that we call\na \"tree game\"; it assigns to each subset of leaves the sum of the weights of\nthe minimal subtree spanned by those leaves. In the context of phylogenetic\ntrees, the leaves are species and this assignment captures the diversity\npresent in the coalition of species considered. We consider the Shapley value\nof tree games and suggest a biological interpretation. We determine the linear\ntransformation M that shows the dependence of the Shapley value on the edge\nweights of the tree, and we also compute a null space basis of M. Both depend\non the \"split counts\" of the tree. Finally, we characterize the Shapley value\non tree games by four axioms, a counterpart to Shapley\u0027s original theorem on\nthe larger class of cooperative games.",
"arxiv_id": "q-bio/0506034",
"authors": [
"Claus-Jochen Haake",
"Akemi Kashiwada",
"Francis Edward Su"
],
"categories": [
"q-bio.QM",
"cs.GT",
"math.CO",
"q-bio.PE"
],
"doi": "10.1007/s00285-007-0126-2",
"journal_ref": "J. Mathematical Biology 56 (2008), 479--497",
"title": "The Shapley Value of Phylogenetic Trees",
"url": "https://arxiv.org/abs/q-bio/0506034"
},
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